I tried this trick to get used to “Good Morning/afternoon”. Saying “Hello” without making an eye contact seemed very difficult so I had to think of a way of starting a conversation on the phone. I had huge blocks on “Good Morning” too. So one day I just called a random place in my area and before the receptionist picked up the phone, I kept repeating “Good Morning” loud and when he picked up I just said it. Then I hung up and called again, this time I tried to say it calmly and I thought that I wouldn’t be able to, but I said it completely fine. Its been 2 months now and I can now say “Good Morning” whenever I want, to who ever I want without stuttering.